PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems
Abstract
Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs [K. T. Mandli et al., PyClaw Software, Version 1.0, http://numerics.kaust.edu.sa/pyclaw/ (2011)]. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The package is further augmented by use of PyWENO for generation of efficient high-order weighted essentially nonoscillatory reconstruction code. The simplicity, capability, and performance of this approach are demonstrated through application to example problems in shallow water flow, compressible flow, and elasticity.
Keywords
MSC codes
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
X. Cai, H. P. Langtangen, and H. Moe, On the performance of the Python programming language for serial and parallel scientific computations, Sci. Program., 13 (2005), pp. 31--56.
2.
D. A. Calhoun, C. Helzel, and R. J. LeVeque, Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains, SIAM Rev., 50 (2008), pp. 723--752.
3.
M. Emmett, PyWENO Software Package, http://memmett.github.com/PyWENO (2011).
4.
J. Enkovaara, N. A. Romero, S. Shende, and J. J. Mortensen, GPAW - massively parallel electronic structure calculations with Python-based software, Procedia Computer Science, 4 (2011), pp. 17--25.
5.
S. Fomel and J. F. Claerbout, Guest editors' introduction: Reproducible research, Comput. Sci. Eng., 11 (1) (2009), pp. 5--7.
6.
J. E. Guyer, D. Wheeler, and J. A. Warren, FiPy: Partial differential equations with Python, Comput. Sci. Eng., 11 (3) (2009), pp. 6--15.
7.
B. Haurwitz, The motion of atmospheric disturbances on a spherical earth, J. Marine Research, 3 (1940), pp. 254--267.
8.
D. I. Ketcheson, Highly efficient strong stability-preserving Runge--Kutta methods with low-storage implementations, SIAM J. Sci. Comput., 30 (2008), pp. 2113--2136.
9.
D. I. Ketcheson and R. J. LeVeque, WENOCLAW: A higher order wave propagation method, in Hyperbolic Problems: Theory, Numerics, Applications, Springer, Berlin, 2008, pp. 609--616.
10.
D. I. Ketcheson and M. Parsani, SharpClaw Software, http://numerics.kaust.edu.sa/sharpclaw (2011).
11.
D. I. Ketcheson, M. Parsani, and R. J. LeVeque, High-Order Wave Propagation Algorithms for General Hyperbolic Systems, http://arxiv.org/abs/1111.3499.
12.
H. P. Langtangen and X. Cai, On the efficiency of Python for high-performance computing: A case study involving stencil updates for partial differential equations, in Modeling, Simulation and Optimization of Complex Processes, H. G. Block, E. Kostina, H. X. Phu, and R. Rannacher, eds., Springer, Berlin, 2008, pp. 337--358.
13.
P. D. Lax and X.-D. Liu, Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comput., 19 (1998), pp. 319--340.
14.
R. J. LeVeque, Wave propagation algorithms for multidimensional hyperbolic systems, J. Comput. Phys., 131 (1997), pp. 327--353.
15.
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, UK, 2002.
16.
R. J. LeVeque and M. J. Berger, Clawpack Software Version \textup4.5, http://www.clawpack.org (2011).
17.
R. J. LeVeque and D. H. Yong, Solitary waves in layered nonlinear media, SIAM J. Appl. Math., 63 (2003), pp. 1539--1560.
18.
K. T. Mandli, D. I. Ketcheson, et al., PyClaw Software, Version 1.0, http://numerics.kaust. edu.sa/pyclaw/ (2011).
19.
K. A. Mardal, O. Skavhaug, G. T. Lines, G. A. Staff, and A. Ødeg\aard, Using Python to solve partial differential equations, Comput. Sci. Eng., 9 (3) (2007), pp. 48--51.
20.
J. Mortensen, L. Hansen, and K. Jacobsen, Real-space grid implementation of the projector augmented wave method, Phys. Rev. B, 71 (2005), 035109.
21.
J. Nilsen, X. Cai, B. Høyland, and H. P. Langtangen, Simplifying the parallelization of scientific codes by a function-centric approach in Python, Computational Science & Discovery, 3 (2010), 015003.
22.
T. Oliphant, NumPy Web Page, http://numpy.scipy.org (2011).
23.
F. Perez, B. E. Granger, and J. D. Hunter, Python: An ecosystem for scientific computing, Comput. Sci. Eng., 13 (2) (2011), pp. 13--21.
24.
M. Quezada de Luna, Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media, M.Sc. thesis, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia, 2011; available online from http://numerics.kaust.edu.sa/papers/quezada-thesis/quezada-thesis.html.
25.
M. Quezada de Luna and D. I. Ketcheson, Radial Solitary Waves in Two-Dimensional Periodic Media, manuscript, 2011.
26.
J. Shi, C. Hu, and C.-W. Shu, A technique of treating negative weights in WENO schemes, J. Comput. Phys., 175 (2002), pp. 108--127.
27.
V. Stodden, M. G. Knepley, C. Wiggins, R. J. LeVeque, D. Donoho, S. Fomel, M. P. Friedlander, M. Gerstein, I. Mitchell, L. L. Ouellette, N. W. Bramble, P. O. Brown, V. Carey, L. DeNardis, R. Gentleman, D. Gezelter, J. A. Goodman, J. E. Moore, F. A. Pasquale, J. Rolnick, M. Seringhaus, and R. Subramanian, Reproducible research: Addressing the need for data and code sharing in computational science, Comput. Sci. Eng., 12 (5) (2010), pp. 8--13.
28.
G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506--517.
29.
J. Thuburn and L. Yong, Numerical simulations of Rossby-Haurwitz waves, Tellus A, 52A (2000), pp. 181--189.
30.
D. L. Williamson, J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations on the sphere, J. Comput. Phys., 102 (1992), pp. 221--224.
Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: C210 - C231
DOI: 10.1137/110856976
ISSN (online): 1095-7197
Copyright
© 2012, Society for Industrial and Applied Mathematics.
History
Submitted: 28 November 2011
Accepted: 8 May 2012
Published online: 15 August 2012
Keywords
MSC codes
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Feature-informed data assimilationJournal of Computational Physics, Vol. 494 | 1 Dec 2023
- Efficient numerical schemes for multidimensional population balance modelsComputers & Chemical Engineering, Vol. 170 | 1 Feb 2023
- Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jumpInternational Journal for Numerical Methods in Fluids, Vol. 94, No. 6 | 23 February 2022
- Data-driven modeling of two-dimensional detonation wave frontsWave Motion, Vol. 109 | 1 Feb 2022
- Learning Quantities of Interest from dynamical systems for observation-consistent inversionComputer Methods in Applied Mechanics and Engineering, Vol. 388 | 1 Jan 2022
- On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equationsPartial Differential Equations and Applications, Vol. 2, No. 6 | 18 October 2021
- Learning Free-Surface Flow with Physics-Informed Neural Networks2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA) | 1 Dec 2021
- A CFD Tutorial in Julia: Introduction to Compressible Laminar Boundary-Layer FlowsFluids, Vol. 6, No. 11 | 5 November 2021
- SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEsJournal of Computational Physics, Vol. 445 | 1 Nov 2021
- Multiscale physics of rotating detonation waves: Autosolitons and modulational instabilitiesPhysical Review E, Vol. 104, No. 2 | 12 August 2021
- Optimal control of an SIR epidemic through finite-time non-pharmaceutical interventionJournal of Mathematical Biology, Vol. 83, No. 1 | 26 June 2021
- Algorithm 1016ACM Transactions on Mathematical Software, Vol. 47, No. 2 | 30 Jun 2021
- Solitary water waves created by variations in bathymetryJournal of Fluid Mechanics, Vol. 917 | 30 April 2021
- A CFD Tutorial in Julia: Introduction to Laminar Boundary-Layer TheoryFluids, Vol. 6, No. 6 | 3 June 2021
- Kinetic Functions for Nonclassical Shocks, Entropy Stability, and Discrete Summation by PartsJournal of Scientific Computing, Vol. 87, No. 2 | 7 April 2021
- Modeling thermodynamic trends of rotating detonation enginesPhysics of Fluids, Vol. 32, No. 12 | 2 December 2020
- py-pde: A Python package for solving partial differential equationsJournal of Open Source Software, Vol. 5, No. 48 | 1 Apr 2020
- Mode-locked rotating detonation waves: Experiments and a model equationPhysical Review E, Vol. 101, No. 1 | 10 January 2020
- Algorithm 997ACM Transactions on Mathematical Software, Vol. 45, No. 3 | 8 August 2019
- CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid DynamicsFluids, Vol. 4, No. 3 | 23 August 2019
- PyFly: A fast, portable aerodynamics simulatorJournal of Computational and Applied Mathematics, Vol. 344 | 1 Dec 2018
- Acoustic shock and acceleration waves in selected inhomogeneous fluidsMechanics Research Communications, Vol. 93 | 1 Oct 2018
- A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epitheliumPLOS Computational Biology, Vol. 13, No. 7 | 28 July 2017
- A Python extension for the massively parallel multiphysics simulation framework waLBerlaInternational Journal of Parallel, Emergent and Distributed Systems, Vol. 31, No. 6 | 14 December 2015
- Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equationsComputers & Mathematics with Applications, Vol. 72, No. 2 | 1 Jul 2016
- High performance Python for direct numerical simulations of turbulent flowsComputer Physics Communications, Vol. 203 | 1 Jun 2016
- Three-Dimensional Mapped-Grid Finite Volume Modeling of Poroelastic-Fluid Wave PropagationSIAM Journal on Scientific Computing, Vol. 38, No. 5 | 13 October 2016
- Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step SizeSIAM Journal on Numerical Analysis, Vol. 54, No. 5 | 8 September 2016
- Clawpack: building an open source ecosystem for solving hyperbolic PDEsPeerJ Computer Science, Vol. 2 | 8 August 2016
- Theory of weakly nonlinear self-sustained detonationsJournal of Fluid Mechanics, Vol. 784 | 3 November 2015
- Claims about the use of software engineering practices in science: A systematic literature reviewInformation and Software Technology, Vol. 67 | 1 Nov 2015
- Diffractons: Solitary Waves Created by Diffraction in Periodic MediaMultiscale Modeling & Simulation, Vol. 13, No. 1 | 31 March 2015
- Integration of FULLSWOF2D and PeanoClaw: Adaptivity and Local Time-Stepping for Complex Overland FlowsRecent Trends in Computational Engineering - CE2014 | 1 Jan 2015
- Programming Languages for Scientific ComputingEncyclopedia of Applied and Computational Mathematics | 21 November 2015
- An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approachJournal of Computational Physics, Vol. 268 | 1 Jul 2014
- Numerical Simulation of Cylindrical Solitary Waves in Periodic MediaJournal of Scientific Computing, Vol. 58, No. 3 | 14 July 2013
- Two-Dimensional Wave Propagation in Layered Periodic MediaSIAM Journal on Applied Mathematics, Vol. 74, No. 6 | 3 December 2014
- Bypassing the Conventional Software Stack Using Adaptable Runtime SystemsEuro-Par 2014: Parallel Processing Workshops | 1 Jan 2014
- High-Order Wave Propagation Algorithms for Hyperbolic SystemsSIAM Journal on Scientific Computing, Vol. 35, No. 1 | 22 January 2013
- Spatially Partitioned Embedded Runge--Kutta MethodsSIAM Journal on Numerical Analysis, Vol. 51, No. 5 | 30 October 2013